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已知数列 \(\left\{ {{a_n}} \right\}\) 的前 \(n\) 项和为 \({S_n}\) , \(2{S_n} = {n^2} + {a_2}n\) .
求 \({a_1}\) , \({a_2}\) ;
参考答案:当 \(n = 1\) 时, \(2{S_1} = 1 + {a_2} = 2{a_1}\) ①,当 \(n = 2\) 时 \(2{S_2} = 4 + 2{a_2} = 2\left( {{a_1} + {a_2}} \right)\) ②,联立①②,得 \({a_1} = 2\) , \({a_2} = 3\) .
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